BLDC Motor Control Example¶

Brushless DC (BLDC) motor with six-step trapezoidal commutation for simple and robust control.

Overview¶

BLDC motors provide: - High torque density (permanent magnet rotor) - Trapezoidal back-EMF (easier commutation than sinusoidal) - Simple six-step (120° conduction) or three-phase commutation - Hall sensor feedback or sensorless operation - Excellent speed control and efficiency - Suitable for appliances, power tools, e-bikes, drones

Specifications¶

Circuit Files¶

• bldc_six_step_basic.ipes - Basic six-step commutation with PWM speed control
• bldc_hall_sensors.ipes - Hall sensor decoding and commutation switching
• bldc_speed_control.ipes - Speed loop with PI controller
• bldc_current_limiting.ipes - Current limit protection during startup
• bldc_sensorless.ipes - Back-EMF zero-crossing detection (advanced)

BLDC Motor Fundamentals¶

Motor Construction¶

The BLDC motor has: - Stator: Three-phase armature windings (A, B, C) fixed around the bore - Rotor: Permanent magnets creating trapezoidal flux distribution - Hall Sensors: Three digital sensors (H1, H2, H3) mounted 120° apart, detect rotor position

Trapezoidal Back-EMF¶

Unlike sinusoidal PMSM, the BLDC has trapezoidal back-EMF:

Where f_trap(θe) is a trapezoidal waveform: - Constant for 120° (±Ke·ω) - Transition for 60° (zero crossing) - Repeats every 360°

This trapezoidal shape allows simple on-off commutation (no sinusoidal modulation).

Six-Step Commutation¶

Hall Sensor Arrangement¶

Three Hall sensors placed 120° mechanical apart provide 6 distinct states:

Note: Each state represents a 60° electrical sector.

Commutation Switching¶

At each Hall transition, switch which two phases are active:

Sector 1 (H1=1,H2=0,H3=1): Phase A → Phase B return
  Top FET:    Q1 (Phase A) ON    → Q3 (Phase B) ON
  Bottom FET: Q5 (Phase B) OFF   → Q6 (Phase C) OFF

Sector 2 (H1=1,H2=0,H3=0): Phase B → Phase C return
  Top FET:    Q1 (Phase A) ON    → Q5 (Phase C) ON
  Bottom FET: Q4 (Phase C) OFF   → Q6 (Phase B) OFF

[... continue for all 6 sectors]

Hard Switching vs. Soft Switching: - Hard switching: Switch only at Hall edge (simple, generates noise) - Commutation advance: Switch 30° before Hall edge for smooth transition (requires accurate timing)

Motor Equations¶

Back-EMF Equation¶

At rated speed ωr (rad/s): $\(e_{ph}(t) = K_e \cdot \omega_r \cdot f_{trap}(θ_e)\)$

RMS back-EMF (per phase): $\(E_{rms} = \frac{K_e \cdot \omega_r}{\sqrt{3}}\)$

For sinusoidal waveform, Ke = (30/π) × Φm × Z / P, where: - Φm: Peak flux per pole (Wb) - Z: Total conductors per phase - P: Number of poles

Torque Production¶

Instantaneous torque: $\(\tau_e(t) = K_t \cdot i_{ph}(t)\)$

Where Kt = Ke (electromagnetic constant).

Average torque (during 120° conduction): $\(\bar{\tau}_e = K_t \cdot I_{avg}\)$

For six-step drive, Iavg is the DC link current (one phase always conducting).

Motor Equations (Phase Model)¶

For a single phase: $\(v_{ph} = R_a \cdot i_{ph} + L_a \frac{di_{ph}}{dt} + e_{ph}(t)\)$

Where: - vph: Applied phase voltage (0V or Vdc depending on switch state) - Ra, La: Phase resistance and inductance - eph: Back-EMF

Control Structure¶

Speed Control Loop¶

           Speed Ref (ωref)
                │
           ┌────┴─────┐
           │    -     │
           └────┬─────┘
                │ ω_error
                ▼
         ┌────────────┐
         │  Speed PI  │ ◄─ Integral Anti-Windup
         │ Controller │
         └────┬───────┘
              │ I_ref_cmd
              ▼
         ┌─────────────────┐
         │ Current Limiter │ ◄─ Peak Current Limit
         │ (max Iref=50A)  │
         └────┬────────────┘
              │ PWM Duty
              ▼
         ┌──────────────┐
         │    PWM on    │ ◄─ Hall Sensors (commutation)
         │  High-Side   │
         │  or Low-Side │
         └────┬─────────┘
              │
              ▼
         ┌──────────────┐
         │   3-Phase    │
         │   Inverter   │
         └────┬─────────┘
              │
              ▼
         ┌──────────────┐
         │  BLDC Motor  │
         └────┬─────────┘
              │
    ┌─────────┴──────────┐
    │ Hall Sensors       │
    │ Speed Estimation   │
    │ (Hall edges → ω)   │
    └─────────┬──────────┘
              │
              └──► Speed Feedback

Current Control Options¶

Option 1: Hysteresis Band Control (Simple)

I_ref = I_max × (PWM_duty / 100)

Actual current feedback:
if i_ph > I_ref + ΔI_hys
    turn OFF PWM
if i_ph < I_ref - ΔI_hys
    turn ON PWM

Option 2: PI Current Loop (Smoother)

I_error = I_ref - I_actual

PWM_duty = K_p × I_error + K_i × ∫I_error dt

Limit: PWM_duty ∈ [0, 100%]

Option 3: Voltage Control (Simplest)

PWM_duty = Duty_ref (directly from speed PI)
No explicit current feedback

Sensorless Operation (Back-EMF Zero-Crossing)¶

For sensorless control, detect the back-EMF zero-crossing of the floating (non-conducting) phase.

Detection Principle¶

During each 120° sector, one phase is floating (not part of the active phase pair).

Example: Sector 1 (A+, B-)

Phase A: Positive high side → floating (not actively driven)
Phase B: Negative low side → floating
Phase C: Floating (detect back-EMF zero crossing)

Back-EMF of phase C:
e_C increases from 0 to peak (positive half-cycle)

Zero-crossing occurs 60° after sector start

Algorithm¶

At each Hall transition:
1. Determine floating phase (the non-conducting one)
2. Read phase voltage via ADC
3. Compare to neutral point (Vdc/2)
4. Detect when e_phase crosses zero (slope change)
5. Apply time delay ≈ 30° (= Ts/6, where Ts = 6 × Thall)
6. Generate next commutation command

Blanking period: First 30° of sector (wait for current decay)
Detection window: 30-60° (look for zero-crossing)
Time delay offset: Advance next commutation by 30°

Startup Procedure (Open-Loop Ramp)¶

For sensorless motors, startup requires special handling:

1. Initial Alignment (500 ms)
   - Apply positive current to phase A
   - Aligns rotor to known position

2. Ramp-Up (1000 ms)
   - Commutate at fixed frequency (e.g., 50 Hz starting)
   - Gradually increase frequency toward expected speed
   - Keep current below limit

3. Transition to Closed-Loop (when speed sufficient)
   - Once back-EMF amplitude exceeds threshold
   - Switch to zero-crossing detection
   - Monitor for successful lock

4. Speed Loop Control
   - Closed-loop frequency modulation
   - Adjust commutation frequency to match motor speed

Design Steps¶

Step 1: Inverter Bridge Selection¶

For 48V DC, 500W: - Peak phase current: Ipk = 500W / (48V × 0.85) ≈ 12A - Average current: Iavg = 10A (at rated power) - Select switches rated for Vce ≥ 60V, Ic ≥ 20A (margin) - Options: low-voltage MOSFET (IRF540, etc.) or IGBT

Deadtime: For 48V low-power, deadtime ≈ 200 ns (minimize shoot-through loss).

Step 2: PWM Frequency Selection¶

Higher frequency → lower torque ripple, higher switching loss Lower frequency → lower loss, more torque ripple

Recommendation: fsw = 20-40 kHz (balance between noise and efficiency)

For commutation, update only on Hall transitions (no PWM within sector).

Step 3: Current Limiting¶

Set maximum phase current to protect switches and battery:

Practical limit: Imax = 50A (power module thermal limit).

Duty cycle limit: $\(D_{max} = \frac{I_{max} \times R_a}{V_{dc}} = \frac{50A \times 0.2Ω}{48V} = 0.21 = 21\%\)$

Step 4: Speed Measurement¶

From Hall Edges:

Hall pulse period = Time between edges
Sector time = Hall period × 6
Motor speed (RPM) = (60 / Sector_time_seconds) × (360 / 360°_mech)

For 6-pole motor (4 pole pairs):
ω_e = 2π × RPM / 60 = π × RPM / 30

Low-Pass Filter Hall speed: Apply soft filter to reduce noise: $\(\omega_{filtered}(k) = 0.9 \times \omega_{filtered}(k-1) + 0.1 \times \omega_{measured}(k)\)$

Step 5: PI Speed Controller Tuning¶

For motor with J = 0.001 kg·m²:

Adjust for stable response (avoid oscillation).

Anti-windup: Limit integral accumulation when duty cycle saturates.

Losses and Efficiency¶

Copper Loss (Joule Heating): $\(P_{cu} = 3 \times I_{rms}^2 \times R_a\)$

For 10A RMS phase current: $\(P_{cu} = 3 \times 10^2 \times 0.2 = 60W\)$

Iron Loss (core saturation): $\(P_{iron} ≈ 20-40W \text{ (at rated speed)}\)$

Mechanical Loss (friction): $\(P_{mech} ≈ 10-20W\)$

Total Loss: Ptotal ≈ 90-120W Efficiency: η ≈ 500W / (500 + 100)W ≈ 83% (typical for this size)

Higher power units achieve 90-95% efficiency.

Exercises¶

1. Hall Sensor Decoding: Verify Hall code to phase-mapping; toggle each phase manually
2. Commutation Sequence: Capture motor phase currents; verify six clean current steps
3. Speed Control: Implement PI speed loop, measure step response (ramp from 0 to 3000 RPM)
4. Current Limiting: Apply load step, observe current limiting and thermal protection
5. Torque Ripple: Measure instantaneous torque (via current × Kt); quantify ripple percentage
6. Load Variation: Test motor under light, medium, and full load; plot efficiency vs. load
7. Sensorless Transition: (Advanced) Implement back-EMF zero-crossing, test startup-to-closed-loop handoff
8. Thermal Simulation: Estimate winding temperature rise from copper loss; design cooling strategy

Related Resources¶

• PMSM Field-Oriented Control
• 402 - Three-Phase Inverter